1. Field of the Invention
The present invention relates to voltage clamping circuits that attempt to maintain a desired clamping voltage in the presence of an undesired series resistance. In particular, the present invention relates to voltage clamping circuits that measure ionic current in biological preparations that are compromised by series resistance. The present invention teaches an improved method to compensate for this series resistance which results in wide bandwidth, zero steady-state error, and high stability.
2. Description of the Prior Art
The Voltage Clamp With Series Resistance
FIG. 1 shows a voltage clamp often used to measure ionic current in biological preparations. Referring to FIG. 1, a low impedance voltage source 5 generates a command voltage Vc. Voltage source 5 is connected to a biological cell 15 through a single cellular microelectrode, patch electrode or pipette elecrode 10, the fabrication of which is well known in the art. Electrode 10 has an electrode series resistance Rs, an electrode voltage Vp, and an electrode current Ip. Cell 15 has a membrane capacitance Cm, a membrane voltage Vm, and a membrane current Im. Im is related to cell membrane conductance changesxe2x80x94a key quantity to measure in order to understand the electrophysiology of the cell being studied. The generation of membrane current Im by the cell is modeled in FIG. 1 by a current source 20.
If Rs is small enough be ignored, voltage source 5 clamps the membrane voltage Vm at Vc and simultaneously shunts Im which would otherwise flow into Cm. In so doing, Im is measured and characterized as a function of Vm.
In practice the large value of Rs ( greater than 10 Mxcexa9) often compromises the effectiveness of the voltage clamp shown in FIG. 1. First, the bandwidth of the voltage clamp and of the current measurement of Im is limited by an access time constant xcfx84a=Rs*Cm, resulting in an uncompensated bandwidth fa=1/xcfx84a. The uncompensated bandwidth is often too low to resolve rapidly activating ionic currents. More importantly, the presence of such large Rs values allows Vm to deviate from the desired command voltage Vc due to the finite voltage drop across Rs. Since Im is often a steep nonlinear function of Vm, such voltage deviation will significantly corrupt the measurement of Im.
Series Resistance Compensation
FIG. 2A shows a common approach to compensate for the effects of series resistance know as standard series resistance compensation (see Electronic Design of the Patch Clamp by F. J. Sigworth, 1983, found in Single-Channel Recording, edited by B. Sakrann an E. Neher, p.29-32.) in which a scaled value of the measured pipette current is used as positive feedback to reduce the effective value of Rs. Referring to FIG. 2A, the voltage clamp of FIG. 1 is shown with the addition of a current measurement means 25, a scaler 35, and a summer 30. Current measurement means 25 measures the electrode current Ip to produce a measured electrode current Ipmeas. Scaler 35 multiplies Ipmeas by a scale factor xcex1*Rs, where scale factor a ranges from 0 to 1, to produce a standard series resistance compensation signal Vcomp. Summer 30 adds the command voltage Vc to Vcomp, thus forming a positive feedback loop.
The effect of standard series resistance compensation is illustrated in FIG. 2B which shows the equivalent circuit of FIG. 2A when Vc is set to zero. Referring to FIG. 2B, Cm is shown shunted by a resistor Reff given by
Reff=(1xe2x88x92xcex1)Rs.xe2x80x83xe2x80x83(E1)
When xcex1=0 Reff=Rs, and as xcex1xe2x86x921, Reffxe2x86x920. Therefore the effect of standard series resistance compensation is to reduce the effective value of Rs to Reff, resulting in a compensated time constant xcfx84comp=Reff*Cm and a compensated bandwidth fcomp=1/xcfx84comp for the voltage clamp. The step response of standard series resistance compensation is shown in FIG. 2C. Referring to FIG. 2C, the response of Vm to a step change in Im is revealed to be an exponential rise (time constant=xcfx84comp) with an asymptotic error voltage given by Im*Reff (ideally, if Reff were zero the error voltage would be zero as well). Significantly, the error voltage is reducedxe2x80x94not eliminatedxe2x80x94by increasing xcex1, accompanied by a simultaneous increase in the compensated bandwidth.
While it would be desirable to filly compensate for Rs by setting xcex1=1, (giving 0 error volage and infinite bandwidth) stability constraints limit the maximum a attainable before undamped oscillations occur. Sigworth shows that this oscillation is related to limited bandwidth of the current measurement circuitry and stray capacitance effects of the electrode. For a well-damped response the current measurement bandwidth needs to bexcx9cten times the volage clamping bandwidth. Consequently, high voltage clamp bandwidth (xcex1 greater than xcx9c0.8) implies very wide current measurement bandwidth that is difficult to achieve in practice.
Even when attempts are made to create a very wide bandwidth current measurement, they are of limited utility due to another factor which reduces stability at high Rs compensation settings: stray capacitance effects of electrode 10. Electrode 10 has stray capacitance (not modeled in FIGS. 1 and 2) which draws current at high frequencies. This current de-stabilizes standard series resistance compensation. (See frequency response analysis in the Appendix of Sherman et. al. 1999. Series Resistance Compensation for Whole-Cell-Patch-Clamp Studies Using a Membrane State Estimator, Biophys. J. 77:2590-2601.) For stable series resistance compensation, it is common practice to compensate for the electrode stray capacitance electronically. The effectiveness of electronic capacitance compensation is compromised at high frequencies, due in part to wide bandwidth requirements, this time in the capacitance compensation circuitry itself. In addition, capacitance compensation performs well when used on a lumped shunt capacitance whereas the electrode stray capacitance is in fact distributed along the length of its immersion depth, in ways that are unpredictable and difficult to characterize mathematically. The distributed nature of the electrode capacitance becomes more pronounced at higher frequencies, which compromises the performance of electronic capacitance compensation. This in turn de-stabilizes standard series resistance compensation at high a settings.
In practice, due both to the difficulties of achieving very wide bandwidth current measurement and of achieving accurate capacitance compensation at high bandwidths, standard series resistance compensation is limited to xcx9c90% (xcex1=0.9).
A common method used to increase the stability of standard Rs compensation is to lowpass filter the signal Vcomp. This approach is used by the Axopatch amplifier series produced by Axon Instruments (Foster City, Calif.), where the xe2x80x9clagxe2x80x9d control sets a time constant for a lowpass filter that acts on the Rs compensation signal. While such lowpass filtering avoids high-frequency oscillations, it is of limited utility since the filter then reduces the voltage clamp bandwidth. (See the Theory section of this patent for a discussion of how lowpass filtering relates to and differs from the present invention).
When working with excitable cells, such as cardiac myocytes responsible for heartbeat generation or nerve cells responsible for nerve signal propagation, a change in Vm of only a few millivolts leads to an extremely large ( greater than 100 fold) and rapid ( less than 300 xcexcs) increase in Im that underlies the generation of the action potential. Thus, when voltage clamping excitable cells it is necessary to maintain the change of Vm in response to a change in Im at less than a few millivolts within a time window of xcx9c200 xcexcs, otherwise an unclamped action potential will be generated, leading to loss of volage control, and corruption of the recorded ionic currents.
The steep voltage dependence of Im versus Vm in excitable cells imposes extremely severe steady-state error requirements that are usually impossible to achieve using standard Rs compensation. To illustrate, consider that a typical patch electrode (Rs)=5 Meg) still has an effective series resistance of 0.5 Mxcexa9 when used with 90% standard Rs compensation (the maximum level that can normally be obtained before the onset of oscillations). Since excitable cells routinely have Im values  greater than 20 nxcex9, the corresponding steady-state error will be  greater than 10 mV (20 nA*0.5 Mxcexa9)xe2x80x94more than enough to trigger an unclamped action potential in the cell. To maintain voltage control, it is necessary to lower series resistance errors in response to ionic current flow to less than 2 mV, which corresponds in this case to 98% Rs compensation and a current measurement bandwidth of  greater than 300 kHz (10* fcompxcx9c30 kHz). Not only is such high bandwidth unattainable due to the technical difficulties listed above, it is actually not needed to successfully voltage clamp rapid ionic current, a voltage clamp bandwidth ofxcx9c10 kHz is sufficient. Therefore, a need exists to provide Rs compensation with very low steady-state error achieved within xcx9c200 xcexcs, but without requiring excessive bandwidth in order to successfully voltage clamp ionic current in excitable cells.
Steady-State Rs Compensation
Moore et. al (Moore, J. W., M Hines, and E. M. Harris. 1984. Compensation for resistance in series with excitable membranes. Biophys. J. 46:507-514) and Strickholm (Strickholm, A. 1995. A single electrode voltage, current and patch-clamp amplifier with complete stable series resistance compensation. J Neurosci. Methods. 61:53-66) each describe similar modifications to standard Rs compensation wherein an electronic bridge is used to subtract the computed membrane capacity current from the signal Vcomp, assuming a fixed membrane conductance; these modifications are collectively referred to here as steady-state Rs compensation. Steady-state Rs compensation has the advantage achieving 100% Rs compensation in the steady-state, thereby eliminating the steady-state error normally associated with standard Rs compensation. The utility of this approach is limited, however, due to the fact that the bridge circuit significantly compromises the voltage clamp bandwidth (see the Theory section of this patent for details as to why this occurs). As a consequence, it takes several milliseconds for the steady-state error to be removed in response to a change in Im using steady-state Rs compensation. This is far too slow to maintain voltage control in excitable cells.
In summary, there exists a need to provide stable series resistance compensation for a voltage clamp that will enable ionic current in excitable cells to be voltage clamped. While prior art techniques exist to compensate for series resistance, they suffer from numerous disadvantages:
(a) Standard Rs compensation requires excessive bandwidth in order to attain low steady-state error. Such high bandwidth is technically difficult to achieve. Also, at high frequencies the distributed nature of the pipette capacitance dominates, limiting stability.
(b) Standard Rs compensation is very prone to instability due to changes in the electrode parameters at high compensation settings.
(c) Steady-state Rs compensation achieves zero steady-state error at the expense of greatly reducing the voltage clamp bandwidth. At such low bandwidth, it is not possible to voltage clamp rapidly activating ionic current.
Due to these disadvantages, it is extremely difficult to voltage clamp rapid ionic current in excitable cells using prior art series resistance compensation techniques.
Accordingly, several objects and advantages of the present invention are:
(a) to compensate for series resistance in a manner that eliminates steady-state error without requiring excessive voltage clamp bandwidth;
(b) to compensate for series resistance in a manner that does not compromise the voltage clamp bandwidth;
(c) to compensate for series resistance in a manner that is not de-stabilized by the distributed capacitance effects of the electrode;
(d) to compensate for series resistance in a manner that is stable with respect to changing electrode characteristics.